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      <h1 class="post-title">剑指offer图专题</h1>

      <div class="post-meta">
        <span class="post-time"> 2021-06-01 </span>
        <div class="post-category">
            <a href="/categories/%E5%89%91%E6%8C%87offer/"> 剑指offer </a>
            </div>
        
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    <div class="post-toc" id="post-toc">
  <h2 class="post-toc-title">Contents</h2>
  <div class="post-toc-content always-active">
    <nav id="TableOfContents">
  <ul>
    <li><a href="#二叉树的下一个节点">二叉树的下一个节点</a>
      <ul>
        <li><a href="#思路">思路</a></li>
      </ul>
    </li>
    <li><a href="#树的子结构">树的子结构</a>
      <ul>
        <li><a href="#题意">题意</a></li>
        <li><a href="#代码">代码</a></li>
        <li><a href="#代码-1">代码</a></li>
      </ul>
    </li>
    <li><a href="#二叉树的镜像">二叉树的镜像</a>
      <ul>
        <li><a href="#写法">写法</a></li>
      </ul>
    </li>
    <li><a href="#对称的二叉树">对称的二叉树</a>
      <ul>
        <li><a href="#写法-1">写法</a></li>
        <li><a href="#代码-2">代码</a></li>
      </ul>
    </li>
    <li><a href="#二叉树中和为sum的路径">二叉树中和为sum的路径</a>
      <ul>
        <li><a href="#heading"></a></li>
      </ul>
    </li>
    <li><a href="#重建二叉树">重建二叉树</a>
      <ul>
        <li><a href="#写法-2">写法</a></li>
        <li><a href="#代码-3">代码</a></li>
      </ul>
    </li>
    <li><a href="#之字形打印二叉树">之字形打印二叉树</a>
      <ul>
        <li><a href="#写法-3">写法</a></li>
      </ul>
    </li>
    <li><a href="#二叉搜索树与双向链表">二叉搜索树与双向链表</a>
      <ul>
        <li><a href="#写法-4">写法</a></li>
      </ul>
    </li>
  </ul>
</nav>
  </div>
</div>
    <div class="post-content">
      <h1 id="二叉树的下一个节点">二叉树的下一个节点</h1>
<h2 id="思路">思路</h2>
<p>中序遍历：先左孩子，然后跟，最后右孩子</p>
<p>这个节点的下一个节点</p>
<ul>
<li>要是这个节点有right
<ul>
<li>跟节点之后就是右节点。</li>
<li>我们走右节点</li>
<li>走右节点，要尽力走左节点</li>
</ul>
</li>
<li>要是这个节点没有right
<ul>
<li>那这个节点属于：上次遍历的右孩子</li>
<li>例如节点D，那我们应该找到这个节点属于哪颗子树：这个节点在这个子树的最右边</li>
<li>找到c之后，输出c的父节点</li>
<li>要是找的节点为空，说明这个节点是最后一个节点</li>
<li><img src="https://tva1.sinaimg.cn/large/0081Kckwly1gkcds2enrkj30my0g640x.jpg" alt="image-20201103230244766"></li>
</ul>
</li>
</ul>
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode *father;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL), father(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="n">TreeNode</span><span class="o">*</span> <span class="n">inorderSuccessor</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">p</span><span class="p">)</span> <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">p</span><span class="p">)</span> <span class="k">return</span> <span class="nb">NULL</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span>
        <span class="p">{</span>
            <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
            <span class="k">while</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
            <span class="k">return</span> <span class="n">p</span><span class="p">;</span>
        <span class="p">}</span>
        <span class="k">while</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">father</span> <span class="o">&amp;&amp;</span> <span class="n">p</span><span class="o">-&gt;</span><span class="n">father</span><span class="o">-&gt;</span><span class="n">right</span> <span class="o">==</span> <span class="n">p</span><span class="p">)</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">father</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">father</span><span class="p">)</span> <span class="k">return</span> <span class="n">p</span><span class="o">-&gt;</span><span class="n">father</span><span class="p">;</span>
        <span class="k">return</span> <span class="nb">NULL</span><span class="p">;</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="树的子结构">树的子结构</h1>
<h2 id="题意">题意</h2>
<p>判断树p2 是不是树p1 的子树</p>
<h2 id="代码">代码</h2>
<ul>
<li>先递归枚举树p1中每一个节点，判断这个节点作为跟节点是不是与p2匹配</li>
<li>写完上面的函数之后，我们再写一个判断是不是匹配的函数，也是递归</li>
</ul>
<h2 id="代码-1">代码</h2>
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="kt">bool</span> <span class="n">hasSubtree</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">pRoot1</span><span class="p">,</span> <span class="n">TreeNode</span><span class="o">*</span> <span class="n">pRoot2</span><span class="p">)</span> <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">pRoot1</span> <span class="o">||</span> <span class="o">!</span><span class="n">pRoot2</span><span class="p">)</span> <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="n">issame</span><span class="p">(</span><span class="n">pRoot1</span> <span class="p">,</span> <span class="n">pRoot2</span><span class="p">))</span> <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
        <span class="k">return</span> <span class="nf">hasSubtree</span><span class="p">(</span><span class="n">pRoot1</span><span class="o">-&gt;</span><span class="n">left</span> <span class="p">,</span><span class="n">pRoot2</span><span class="p">)</span> <span class="o">||</span> <span class="n">hasSubtree</span><span class="p">(</span><span class="n">pRoot1</span><span class="o">-&gt;</span><span class="n">right</span> <span class="p">,</span> <span class="n">pRoot2</span><span class="p">);</span>
    <span class="p">}</span>
    <span class="kt">bool</span> <span class="nf">issame</span><span class="p">(</span><span class="n">TreeNode</span> <span class="o">*</span><span class="n">p1</span><span class="p">,</span><span class="n">TreeNode</span><span class="o">*</span><span class="n">p2</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">p2</span><span class="p">)</span> <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">p1</span> <span class="o">||</span> <span class="n">p1</span><span class="o">-&gt;</span><span class="n">val</span> <span class="o">!=</span> <span class="n">p2</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span> <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
        <span class="k">return</span> <span class="n">issame</span><span class="p">(</span><span class="n">p1</span><span class="o">-&gt;</span><span class="n">left</span> <span class="p">,</span> <span class="n">p2</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span>  <span class="o">&amp;&amp;</span> <span class="n">issame</span><span class="p">(</span><span class="n">p1</span><span class="o">-&gt;</span><span class="n">right</span> <span class="p">,</span> <span class="n">p2</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="二叉树的镜像">二叉树的镜像</h1>
<h2 id="写法">写法</h2>
<p>递归：递归镜像左子树、递归镜像右子树</p>
<p>使用递归把左右子树处理完之后，swap俩颗子树</p>
<div class="highlight"><div class="chroma">
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="kt">void</span> <span class="n">mirror</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">root</span><span class="p">)</span> <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">root</span><span class="p">)</span> <span class="k">return</span><span class="p">;</span>
        <span class="n">mirror</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">),</span><span class="n">mirror</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
        <span class="n">swap</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="对称的二叉树">对称的二叉树</h1>
<h2 id="写法-1">写法</h2>
<p>写一个函数dfs(p,q) ：返回，p、q子树是不是对称</p>
<ul>
<li>p的left == q的right</li>
<li>p的right== q的left</li>
</ul>
<h2 id="代码-2">代码</h2>
<div class="highlight"><div class="chroma">
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="kt">bool</span> <span class="n">isSymmetric</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">root</span><span class="p">)</span> <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">root</span><span class="p">)</span> <span class="k">return</span> <span class="nb">true</span><span class="p">;</span>
        <span class="k">return</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
    <span class="p">}</span>
    <span class="kt">bool</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span><span class="n">p</span><span class="p">,</span><span class="n">TreeNode</span><span class="o">*</span><span class="n">q</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">p</span> <span class="o">||</span> <span class="o">!</span><span class="n">q</span><span class="p">)</span> <span class="k">return</span> <span class="n">p</span><span class="o">==</span><span class="n">q</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">val</span> <span class="o">!=</span> <span class="n">q</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span> <span class="k">return</span> <span class="nb">false</span><span class="p">;</span>
        <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="n">q</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span> <span class="o">&amp;&amp;</span> <span class="n">dfs</span><span class="p">(</span><span class="n">p</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="n">q</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="二叉树中和为sum的路径">二叉树中和为sum的路径</h1>
<h2 id="heading"></h2>
<div class="highlight"><div class="chroma">
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<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="n">res</span><span class="p">;</span>
    <span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="n">temp</span><span class="p">;</span>
    <span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span> <span class="n">findPath</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">root</span><span class="p">,</span> <span class="kt">int</span> <span class="n">sum</span><span class="p">)</span> <span class="p">{</span>
        
        <span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="n">sum</span><span class="p">);</span>
        <span class="k">return</span> <span class="n">res</span><span class="p">;</span>
        
    <span class="p">}</span>
    <span class="kt">void</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">TreeNode</span> <span class="o">*</span><span class="n">u</span><span class="p">,</span><span class="kt">int</span> <span class="n">sum</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">u</span><span class="p">)</span> <span class="k">return</span> <span class="p">;</span>
        
        <span class="n">temp</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
        <span class="n">sum</span><span class="o">-=</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">&amp;&amp;</span> <span class="o">!</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span> <span class="o">&amp;&amp;</span> <span class="o">!</span><span class="n">sum</span><span class="p">)</span> <span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">temp</span><span class="p">);</span>
        
        <span class="n">dfs</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="n">sum</span><span class="p">);</span>
        <span class="n">dfs</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="n">sum</span><span class="p">);</span>
        <span class="n">sum</span><span class="o">+=</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
        <span class="n">temp</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="重建二叉树">重建二叉树</h1>
<h2 id="写法-2">写法</h2>
<ul>
<li>根据前序遍历的第一个元素为根节点，然后在中序遍历中找到这个元素，确定好左子树的长度</li>
<li>接下来新建一个根节点</li>
<li>然后递归找左子树、右子树</li>
<li>然后根节点的left、right连接到这俩子树</li>
<li>然后返回root节点</li>
<li>递归的过程要传入：前序遍历的区间，对应的中序遍历的区间</li>
<li>然后递归过程中：要确定左子树的区间，右子树的区间
<ul>
<li>可以加一个遍历记录一下左子树的长度</li>
</ul>
</li>
</ul>
<h2 id="代码-3">代码</h2>
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<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="kt">int</span><span class="o">&gt;</span><span class="n">hash</span><span class="p">;</span>
    <span class="n">TreeNode</span><span class="o">*</span> <span class="nf">buildTree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&amp;</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&amp;</span> <span class="n">inorder</span><span class="p">)</span> <span class="p">{</span>
        <span class="kt">int</span> <span class="n">n</span><span class="o">=</span><span class="n">preorder</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="n">n</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
        <span class="p">{</span>
            <span class="n">hash</span><span class="p">[</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span>
        <span class="p">}</span>
        <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="n">inorder</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="n">n</span><span class="p">);</span>
        
    <span class="p">}</span>
    <span class="n">TreeNode</span> <span class="o">*</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&amp;</span><span class="n">pre</span><span class="p">,</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&amp;</span><span class="n">in</span><span class="p">,</span><span class="kt">int</span>  <span class="n">pl</span><span class="p">,</span><span class="kt">int</span> <span class="n">pr</span><span class="p">,</span><span class="kt">int</span> <span class="n">il</span><span class="p">,</span><span class="kt">int</span> <span class="n">ir</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="n">pl</span><span class="o">&gt;</span><span class="n">pr</span><span class="p">)</span> <span class="k">return</span> <span class="nb">NULL</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="n">il</span><span class="o">&gt;</span><span class="n">ir</span><span class="p">)</span> <span class="k">return</span> <span class="nb">NULL</span><span class="p">;</span>
        <span class="kt">int</span> <span class="n">k</span><span class="o">=</span><span class="n">hash</span><span class="p">[</span><span class="n">pre</span><span class="p">[</span><span class="n">pl</span><span class="p">]]</span><span class="o">-</span> <span class="n">il</span><span class="o">+</span><span class="mi">1</span><span class="p">;</span>
        <span class="n">TreeNode</span> <span class="o">*</span> <span class="n">root</span> <span class="o">=</span> <span class="k">new</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">pre</span><span class="p">[</span><span class="n">pl</span><span class="p">]);</span>
        <span class="k">auto</span> <span class="n">left</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">pre</span><span class="p">,</span><span class="n">in</span><span class="p">,</span><span class="n">pl</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">pl</span><span class="o">+</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="n">il</span><span class="p">,</span><span class="n">il</span><span class="o">+</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">);</span>
        <span class="k">auto</span> <span class="n">right</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">pre</span><span class="p">,</span><span class="n">in</span><span class="p">,</span><span class="n">pl</span><span class="o">+</span><span class="n">k</span><span class="p">,</span><span class="n">pr</span><span class="p">,</span><span class="n">il</span><span class="o">+</span><span class="n">k</span><span class="p">,</span><span class="n">ir</span><span class="p">);</span>
        <span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="o">=</span><span class="n">left</span><span class="p">;</span>
        <span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="o">=</span><span class="n">right</span><span class="p">;</span>
        <span class="k">return</span> <span class="n">root</span><span class="p">;</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="之字形打印二叉树">之字形打印二叉树</h1>
<h2 id="写法-3">写法</h2>
<p>每一层后面加一个NULL标记，队列里面取到NULL意味着这一层结束</p>
<p>上诉操作，前提：队列里面有元素，否则一直加NULL，队列停不下来</p>
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span> <span class="n">printFromTopToBottom</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">root</span><span class="p">)</span> <span class="p">{</span>
        
        <span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span> <span class="n">res</span><span class="p">;</span>
        <span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="n">temp</span><span class="p">;</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">root</span><span class="p">)</span> <span class="k">return</span> <span class="n">res</span><span class="p">;</span>
        <span class="n">queue</span><span class="o">&lt;</span><span class="n">TreeNode</span> <span class="o">*</span> <span class="o">&gt;</span><span class="n">q</span><span class="p">;</span>
        <span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
        <span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="nb">NULL</span><span class="p">);</span>
        <span class="kt">bool</span> <span class="n">ok</span><span class="o">=</span><span class="nb">true</span><span class="p">;</span>
        <span class="k">while</span><span class="p">(</span><span class="n">q</span><span class="p">.</span><span class="n">size</span><span class="p">())</span>
        <span class="p">{</span>
            <span class="k">auto</span> <span class="n">t</span><span class="o">=</span><span class="n">q</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
            <span class="n">q</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
           
            <span class="k">if</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
            <span class="p">{</span>
                <span class="n">temp</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
                <span class="k">if</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span> <span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
                <span class="k">if</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span> <span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">t</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
            <span class="p">}</span>
            <span class="k">else</span><span class="p">{</span>
                <span class="k">if</span><span class="p">(</span><span class="n">q</span><span class="p">.</span><span class="n">size</span><span class="p">()</span> <span class="p">)</span><span class="n">q</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="nb">NULL</span><span class="p">);</span>
                <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">ok</span><span class="p">)</span> <span class="n">reverse</span><span class="p">(</span><span class="n">temp</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="n">temp</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
                <span class="n">ok</span><span class="o">=!</span><span class="n">ok</span><span class="p">;</span>
                <span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">temp</span><span class="p">);</span>
                <span class="n">temp</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
            <span class="p">}</span>
        <span class="p">}</span>
        <span class="k">return</span> <span class="n">res</span><span class="p">;</span>
        
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
</div>
</div><h1 id="二叉搜索树与双向链表">二叉搜索树与双向链表</h1>
<h2 id="写法-4">写法</h2>
<p>递归一个节点，返回值是一个pair，然后处理这个pair连接这个跟节点</p>
<p>分情况：有没有跟节点、有无左右节点</p>
<p>然后处理</p>
<div class="highlight"><div class="chroma">
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<td class="lntd">
<pre class="chroma"><code class="language-cpp" data-lang="cpp"><span class="cm">/**
</span><span class="cm"> * Definition for a binary tree node.
</span><span class="cm"> * struct TreeNode {
</span><span class="cm"> *     int val;
</span><span class="cm"> *     TreeNode *left;
</span><span class="cm"> *     TreeNode *right;
</span><span class="cm"> *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
</span><span class="cm"> * };
</span><span class="cm"> */</span>
<span class="k">class</span> <span class="nc">Solution</span> <span class="p">{</span>
<span class="k">public</span><span class="o">:</span>
    <span class="n">TreeNode</span><span class="o">*</span> <span class="n">convert</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">root</span><span class="p">)</span> <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">root</span><span class="p">)</span> <span class="k">return</span> <span class="nb">NULL</span><span class="p">;</span>
        <span class="k">auto</span> <span class="n">res</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
        <span class="k">return</span> <span class="n">res</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
    <span class="p">}</span>
    <span class="n">pair</span><span class="o">&lt;</span><span class="n">TreeNode</span> <span class="o">*</span> <span class="p">,</span><span class="n">TreeNode</span> <span class="o">*&gt;</span> <span class="n">dfs</span><span class="p">(</span><span class="n">TreeNode</span><span class="o">*</span> <span class="n">u</span><span class="p">)</span>
    <span class="p">{</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">&amp;&amp;</span> <span class="o">!</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span> <span class="k">return</span> <span class="n">make_pair</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">u</span><span class="p">);</span>
        <span class="k">if</span><span class="p">(</span><span class="o">!</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">&amp;&amp;</span> <span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">){</span>
            <span class="k">auto</span> <span class="n">right</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
            <span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="o">=</span><span class="n">right</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
            <span class="n">right</span><span class="p">.</span><span class="n">first</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">=</span> <span class="n">u</span><span class="p">;</span>
            <span class="k">return</span> <span class="nf">make_pair</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">right</span><span class="p">.</span><span class="n">second</span><span class="p">);</span>
        <span class="p">}</span>
        <span class="k">else</span> <span class="nf">if</span><span class="p">(</span><span class="o">!</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span> <span class="o">&amp;&amp;</span> <span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">){</span>
            <span class="k">auto</span> <span class="n">left</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
            <span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">=</span> <span class="n">left</span><span class="p">.</span><span class="n">second</span><span class="p">;</span>
            <span class="n">left</span><span class="p">.</span><span class="n">second</span> <span class="o">-&gt;</span> <span class="n">right</span> <span class="o">=</span> <span class="n">u</span><span class="p">;</span>
            <span class="n">make_pair</span><span class="p">(</span><span class="n">left</span><span class="p">.</span><span class="n">first</span><span class="p">,</span><span class="n">u</span><span class="p">);</span>
        <span class="p">}</span>
        <span class="k">else</span><span class="p">{</span>
            <span class="k">auto</span> <span class="n">left</span><span class="o">=</span><span class="n">dfs</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
            <span class="k">auto</span> <span class="n">right</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
            <span class="n">u</span><span class="o">-&gt;</span><span class="n">right</span><span class="o">=</span><span class="n">right</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
            <span class="n">right</span><span class="p">.</span><span class="n">first</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">=</span> <span class="n">u</span><span class="p">;</span>
            <span class="n">u</span><span class="o">-&gt;</span><span class="n">left</span> <span class="o">=</span> <span class="n">left</span><span class="p">.</span><span class="n">second</span><span class="p">;</span>
            <span class="n">left</span><span class="p">.</span><span class="n">second</span> <span class="o">-&gt;</span> <span class="n">right</span> <span class="o">=</span> <span class="n">u</span><span class="p">;</span>
            <span class="k">return</span> <span class="nf">make_pair</span><span class="p">(</span><span class="n">left</span><span class="p">.</span><span class="n">first</span><span class="p">,</span><span class="n">right</span><span class="p">.</span><span class="n">second</span><span class="p">);</span>
        <span class="p">}</span>
    <span class="p">}</span>
<span class="p">};</span>
</code></pre></td></tr></table>
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